How to completely remove personal files on the computer?

Sombody have an old computer, for example,serviceable Apple eMac that they would like to give to another. So they want to deleted all their files but am leery of having some of personal info still retrievable. Would deleting and reloading the OS be of value, or are there other steps to take?

For peace of mind, I suggest to use a secure file-wiping utility and erase the entire drive using it. Then, presuming you have the original disks, you can reinstall the operating system.

A file-wiping utility erases files, and then overwrites the portions of the hard disk they occupied, as well as free space on the drive, multiple times, usually with zeroes, so the original contents can't be recovered.

I don't know which version of the Mac operating system you have, but the original disks that come with most Macs contain a program called Disk Utility that can do this, if you select the 'Erase' option and then the 'Erase Free Space' option. You will have to first boot the computer up from the operating system disk.